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CNN-based End-to-End Adaptive Controller with Stability Guarantees

Myeongseok Ryu, Kyunghwan Choi

TL;DR

This letter proposes a convolutional neural network (CNN)-based adaptive controller that determines control input directly from historical sensor data (in an end-to-end process) and has a superior tracking performance to that of a deep neural network (DNN)-based adaptive controller.

Abstract

This letter proposes a convolutional neural network (CNN)-based adaptive controller wtih three notable features: 1) it determines control input directly from historical sensor data (in an end-to-end process); 2) it learns the desired control policy during real-time implementation without using a pretrained network (in an online adaptive manner); and 3) the asymptotic tracking error convergence is proven during the learning process (to deliver a stability guarantee). An adaptive law for learning the desired control policy is derived using the gradient descent optimization method, and its stability is analyzed based on the Lyapunov approach. A simulation study using a control-affine nonlinear system demonstrated that the proposed controller exhibits these features, and its performance can be tuned by manipulating the design parameters. In addition, it is shown that the proposed controller has a superior tracking performance to that of a deep neural network (DNN)-based adaptive controller.

CNN-based End-to-End Adaptive Controller with Stability Guarantees

TL;DR

This letter proposes a convolutional neural network (CNN)-based adaptive controller that determines control input directly from historical sensor data (in an end-to-end process) and has a superior tracking performance to that of a deep neural network (DNN)-based adaptive controller.

Abstract

This letter proposes a convolutional neural network (CNN)-based adaptive controller wtih three notable features: 1) it determines control input directly from historical sensor data (in an end-to-end process); 2) it learns the desired control policy during real-time implementation without using a pretrained network (in an online adaptive manner); and 3) the asymptotic tracking error convergence is proven during the learning process (to deliver a stability guarantee). An adaptive law for learning the desired control policy is derived using the gradient descent optimization method, and its stability is analyzed based on the Lyapunov approach. A simulation study using a control-affine nonlinear system demonstrated that the proposed controller exhibits these features, and its performance can be tuned by manipulating the design parameters. In addition, it is shown that the proposed controller has a superior tracking performance to that of a deep neural network (DNN)-based adaptive controller.
Paper Structure (18 sections, 1 theorem, 31 equations, 3 figures, 1 table)

This paper contains 18 sections, 1 theorem, 31 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Controller Design
  4. Convolutional Layers
  5. Fully-Connected Layers
  6. Control Law Development
  7. Network Input Matrix Design
  8. Weight Adaptation Law
  9. Jacobians with respect to Convolutional Layers
  10. Jacobians with respect to Fully-connected Layers
  11. Derivation of Adaptation Laws
  12. Stability Analysis
  13. Simulations
  14. Effects of Design Parameters
  15. CNN vs. DNN
  16. ...and 3 more sections

Key Result

Theorem 1

For the dynamical system in eq: model dynamics, the proposed controller in eq: proposed ctrl and adaptation law eq: adaptation law ensure asymptotic tracking error convergence, in the sense that $e\to0$ as $t\to \infty$, provided that $\beta_1\beta_2^2+ \bar{\Delta} \le k_s$ where $\beta_1=\rho||\Ga

Figures (3)

  • Figure 1: CNN architecture used in the proposed controller.
  • Figure 2: Tracking errors of (a) CNN1, (b) CNN2, (c) CNN3, (d) CNN4, (e) CNN5, and (f) DNN. The blue and red solid lines represent $e_1$ and $e_2$, respectively.
  • Figure 3: Control results of CNN1 (blue solid line) and DNN (red solid line) under a sudden change in the system at $3$ s. The green dash-dotted line denotes the desired trajectory.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2